User Caciulacdlac on Bulbapedia has compiled a list of Pokemon that appeared before their generation starts airing. I assume the Japan broadcast date is used as the criteria.
The whole answer below is mostly based on the link above, and several other articles on Bulbapedia.
All the dates cited below will be Japan broadcast dates. Episode numbering will follow the numbering used by Bulbapedia.
Episode 117, aired on October 14, 1999, marks the start of the The Johto Journeys (season 3), and also the start of generation II. The Pokemon listed below are from generation II, but appeared in the anime before the journey to Johto started.
- Ho-Oh: Episode 001: Pokémon - I Choose You! (April 1, 1997)
- Togepi: Episode 050: Who Gets to Keep Togepi? (June 25, 1998)
- Marill, Snubbull: Pikachu Shorts 01: Pikachu's Vacation (July 18, 1998)
- Donphan: Movies 01: Mewtwo Strikes Back (July 18, 1998)
- Ledyba, Elekid1, Bellossom, Hoothoot: Pikachu Shorts 04: Pikachu's Rescue Adventure (July 17, 1999)
1 Elekid also appeared earlier in Tracey's sketch in Episode 103 - Misty Meets Her Match (July 1, 1999)
- Lugia, Slowking: Movies 2: The Power of One (July 17, 1999)
The first episode of Advanced Generation series, aired on November 21, 2002, marks the start of Pokémon: Advanced season (season 6), and also the start of generation III. The Pokemon listed below are from generation III, but appeared in the anime before generation III (to Hoenn) started.
- Kecleon: Episode 205: The Kecleon Caper (July 5, 2001)
- Azurill, Wailmer: Pikachu Shorts 10: Pikachu's PikaBoo (July 7, 2001)
- Wynaut: Episode 252: Fangs for Nothin' (June 13, 2002)
- Duskull, Volbeat: Pikachu Shorts 11: Camp Pikachu (July 13, 2002)
- Latias, Latios: Movies 05: Pokémon Heroes (July 13, 2002)
- Blaziken: Episode 265: Pop Goes The Sneasel (September 12, 2002)
- Sharpedo, Seedot, Shroomish, Lotad, Zigzagoon: Episode 272: Johto Photo Finish (October 31, 2002)
- Wingull, Pelipper: Episode 274: Hoenn Alone! (November 14, 2002)
The first episode of Diamond and Pearl series, aired on September 28, 2006, marks the start of Pokemon: Diamond and Pearl season (season 10) and also the start of generation IV. The Pokemon listed below are from generation IV, but appeared in the anime before the journey to Sinnoh started.
- Munchlax: Movies 07: Destiny Deoxys (July 17, 2004)
- Lucario, Bonsly, Weavile, Mime Jr.: Movies 08: Lucario and the Mystery of Mew (July 16, 2005)
- Manaphy, Mantyke, Buizel, Chatot: Movies 09: Pokémon Ranger and the Temple of the Sea (July 15, 2006)
- Electivire: Advanced Generation Episode 192: Home is Where the Start Is! (September 14, 2006)
The first episode of Best Wishes series, aired on September 23, 2010, marks the start of generation V. The Pokemon listed below are from generation V, but appeared in the anime before the journey to Unova started.
The first episode of XY Series, aired on October 17, 2013, marks the start of generation VI. The Pokemon listed below are from generation VI, but appeared in the anime before the journey to Kalos started.